Partial theta function identities from Wang and Ma's conjecture

TL;DR

This paper confirms Wang and Ma's conjecture related to generalizations of Andrews-Warnaar identities and uses it to express series via partial theta functions, leading to new identities.

Contribution

The paper proves Wang and Ma's conjecture and derives new partial theta function identities based on this result.

Findings

Confirmed Wang and Ma's conjecture.

Expressed series using partial theta functions.

Constructed new partial theta function identities.

Abstract

Recently, Wang and Ma propose a conjecture associated with the possible generalization of Andrews-Warnaar identities. It is confirmed in this paper. As the applications of this conjecture, we prove that a family of series can be expressed by the partial theta functions and construct some new partial theta function identities.